At the onset of his arrival, Revered Hale enters Salem with confidence carrying books on the subjects of spirits and witches. He takes the subject of witchcraft very seriously, and even comments about how it is best not to jump to conclusions on the matter. Hale insists that he will discover the truth in his investigation; however, he enters Salem somewhat jaded, not knowing the full scope of the property disputes and struggles for power within the church/community. Throughout the course of his investigation, and the court proceedings, Hale initially believes the girls, and their claims of witchcraft against others. Hale’s belief in the girls’ accusations is not entirely a fault all his own, he entered the town a bit over zealous. The first change we see sparked in Hale is in Act Two when Proctor confesses to Hale that Abigail told him that the sickness was not a result of witchcraft. After Proctor tells Hale this, and agrees to testify, they learn that Goody Nurse, Goody Corey, and Elizabeth Proctor have been accused. Hale tells John that he will testify on Elizabeth’s behalf in court, but also seems to be awestruck by the supposed “proof” of Elizabeth’s crime. Near the end of Act Two, after pleading for patience of the courts with John Proctor, Hale makes this statement to Giles and Francis, “I Pray God open up our eyes.” The next time Hale is seen(in Act Three), it seems as though his prayers have been answered, because he seems to be closer to the truth than he has been at any other point in the play. Hale pleads for careful consideration from the courts as he says that he has “signed away…soul[s]…” and begs Danforth for careful consideration in the case that Proctor and Mary Warren, Corey, and Nurse have some to plead. Towards the end of Act Three, Hale becomes increasingly vocal in his support for the evidence Proctor presents and his insistence on the complete fabrication of the accusations by Abigail, even at one point insisting that she has “gone wild.” At the very end of Act Three, Hale denounces the court proceedings, quits the court, and then exits slamming the door behind him. Interestingly enough, in Act Four, we see Hale return to Salem to “plead” with those condemned to die. He makes the statement that he thinks that God would not punish the condemned for “confessing” to a crime they did not commit any more than he would for them dying for a crime they didn’t commit. He tries to explain to the accused that even though they know the truth, they will have to lie to save their lives, and he encourages them to do so. In the end, we see Reverend Hale as a man who is a hundred and eighty degrees different, figuratively speaking, than he was at the start of the play. Ironically enough, even though he disagrees with the court, and knows the truth about the witch trails, as minister who initially confirmed the validity of the later to be known false accusations, he has no authority to save those affected by his misjudgment. He holds himself responsible, and maybe he should, but regardless of any impending doom that awaits those condemned, he still knows that their deaths are without justification. At the end we see, as John Proctor called him earlier in the play, a truly broken minister; one who now has pause to question the very foundation of everything that was only a short time ago so certain to him upon his initial arrival in Salem.

The previous answer was quite thorough. I would only add that part of the reason that Hale does change is that he is forced to recognize the duplicity that exists within individual actions. What would drive Hale to such a point could be summed up in a line from Yeats' poem, "The Second Coming:"

the best lack all conviction/ while the worst are filled with passionate intensity.

For Hale, he cannot understand how individuals with so much passion can represent the very evil he is committed to stamping out of Salem and of the world. There is a singularity within Hale that is fundamentally challenged by the end of the play. For example, in Act II, when Hale visits the Proctor home, he is about to leave before Francis Nurse and Giles Corey bust in with the news that their wives have been arrested. Prior to leaving, Hale tells John and Elizabeth that the path to their salvation lies in showing deference to the church and Reverend Parris, attending it more often especially on the Sabbath, and having their last child baptized. In Hale's mind, there is a convergence with religious purity and the institution. He cannot fathom that there would be a disconnect. It is this same reasoning that compels him to investigate Martha Corey after Giles talks about her reading. Hale simply cannot see something wrong in an investigation as he believes it is being conducted by flatly religious people. Hale changes in that he is forced to understand that there might be a disconnect in the psyche of individuals. The most spiritual of people might not be the ones that are considered to be so and the ones who are considered to be so might not be. Hale struggles with this, as he breaks from the court and seeks to pursue a more "grass roots" approach to ridding the town of witches in his desire to extract confessions. It is for this reason that he seems to not want to understand Proctor's motivation at the end. If he does understand it and accept it, the result would be a fundamental shift in that idea that there is a duality or a complexity within human nature and that the singularity that has dominated his life is not evident in an intricate setting. It is here where Hale undergoes the greatest amount of change.